\documentclass[graybox]{svmult}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{soul}  % highlight text using \hl
\usepackage{verbatim}  % multiline comments
\usepackage{subfig}

\begin{document}

\title{Sunspots}
\author{Ricardo Cruz \and Renato Fernandes \and Alberto Pinto}
\institute{
Ricardo Cruz \email{ricardo.pdm.cruz@gmail.com}
\and Renato Fernandes \email{renatodsfernandes@gmail.com}
\and Alberto Pinto, University of Porto \email{aapinto@fc.up.pt}
}

\maketitle

\abstract{
sun spots are spots in the sun .. bhp fit ..
}

\section{Introduction}

\begin{figure}
\centering
\includegraphics[trim=0 75px 0 75px, clip, width=1\textwidth]{sunspots.jpg}
\caption{Sunspots picture.}
\label{fig:sunspots-picture}
\end{figure}


\section{Data}

\begin{figure}
\centering
\includegraphics[width=\textwidth]{sunspots-means.pdf}
\caption{Sunspots means.}
\label{fig:sunspots-means}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=\textwidth]{sunspots-deviations.pdf}
\caption{Sunspots deviations.}
\label{fig:sunspots-deviations}
\end{figure}

All data processing and figures were created using R \cite{ref:R}. \footnote{Data from: \url{http://solarscience.msfc.nasa.gov/SunspotCycle.shtml}}



\begin{figure}
\centering
\includegraphics[width=\linewidth]{sunspots-lambdas-hist.pdf}
\caption{Fitting of several lambdas for the sunspots for $\mathbf{w}_1 = (-)$ (decreasing flows of memory 1). Top: the resulting transformation on the time series. Bottom: the histogram (in red: $\mathcal{N}(0,1)$, and blue: BHP). Note: $\lambda = 1$ implies only an affine transformation of the data.}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=\linewidth]{sunspots-lambdas-fit.pdf}
\caption{The Kolmogorov-Smirnov statistic for the BHP and Normal distribution when using different lambdas. $\lambda^*$ (for which the statistic is minimize) is represented as a red dot.}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=\linewidth]{sunspots-lambdas-time.pdf}
\caption{We fit $\lambda^*$ across time sections (for the BHP). For each year, we estimate $\lambda^*$ by looking at the distribution of flows within the preceding $\sim 11$ years up to that year ($133$ are Earth months for a full sun year, so a sun year is roughly $133/12 \approx 11$ years). The red horizontal line is $\lambda^*$ for the entire data. The Dalton Minimum heating period (one of the periods when sunpots were irregular) is represented in gray (1790-1830).}
\label{fig:paiva-lambdas-time}
\end{figure}


\begin{thebibliography}{99}

\bibitem{artigo4}
	R. Gon{c}calves, A. Pinto, and N. Stollenwerk,
    \emph{Cycles and universality in sunspot numbers fluctuations}.
	Astrophys. J. 691, pp. 1583-1586, 2009.

\bibitem{ref:R}
  R Core Team,
  \emph{R: A Language and Environment for Statistical Computing}.
  R Foundation for Statistical Computing,
  2014.

\end{thebibliography}

\end{document}

